Liouville theorems for a family of very degenerate elliptic nonlinear operators
| Autor: | Fabiana Leoni, Giulio Galise, Isabeau Birindelli |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Hessian matrix
Pure mathematics viscosity solutions Applied Mathematics Operator (physics) 010102 general mathematics Degenerate energy levels fully nonlinear degenerate elliptic equations Liouville type results 01 natural sciences 010101 applied mathematics Nonlinear system symbols.namesake Elliptic operator symbols 0101 mathematics Degeneracy (mathematics) Laplace operator Analysis Eigenvalues and eigenvectors Mathematics |
| Zdroj: | Nonlinear Analysis. 161:198-211 |
| ISSN: | 0362-546X |
| DOI: | 10.1016/j.na.2017.06.002 |
| Popis: | We prove nonexistence results of Liouville type for nonnegative viscosity solutions of some equations involving the fully nonlinear degenerate elliptic operators P k ± , defined respectively as the sum of the largest and the smallest k eigenvalues of the Hessian matrix. For the operator P k + we obtain results analogous to those which hold for the Laplace operator in space dimension k . Whereas, owing to the stronger degeneracy of the operator P k − , we get totally different results. |
| Databáze: | OpenAIRE |
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